Geodesic
$C$-Gorenstein projective, injective and flat modules
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1109-1129 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

By analogy with the projective, injective and flat modules, in this paper we study some properties of $C$-Gorenstein projective, injective and flat modules and discuss some connections between $C$-Gorenstein injective and $C$-Gorenstein flat modules. We also investigate some connections between $C$-Gorenstein projective, injective and flat modules of change of rings.
By analogy with the projective, injective and flat modules, in this paper we study some properties of $C$-Gorenstein projective, injective and flat modules and discuss some connections between $C$-Gorenstein injective and $C$-Gorenstein flat modules. We also investigate some connections between $C$-Gorenstein projective, injective and flat modules of change of rings.
Classification : 13D07, 16E65
Keywords: $C$-Gorenstein projective module; $C$-Gorenstein injective module; $C$-Gorenstein flat module 
@article{CMJ_2010_60_4_a19,
     author = {Yang, Xiao Yan and Liu, Zhong Kui},
     title = {$C${-Gorenstein} projective, injective and flat modules},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1109--1129},
     year = {2010},
     volume = {60},
     number = {4},
     mrnumber = {2738973},
     zbl = {1224.13014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a19/}
}
TY  - JOUR
AU  - Yang, Xiao Yan
AU  - Liu, Zhong Kui
TI  - $C$-Gorenstein projective, injective and flat modules
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 1109
EP  - 1129
VL  - 60
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a19/
LA  - en
ID  - CMJ_2010_60_4_a19
ER  - 
%0 Journal Article
%A Yang, Xiao Yan
%A Liu, Zhong Kui
%T $C$-Gorenstein projective, injective and flat modules
%J Czechoslovak Mathematical Journal
%D 2010
%P 1109-1129
%V 60
%N 4
%U http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a19/
%G en
%F CMJ_2010_60_4_a19
Yang, Xiao Yan; Liu, Zhong Kui. $C$-Gorenstein projective, injective and flat modules. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 1109-1129. http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a19/

[1] Christensen, L. W., Frankild, A., Holm, H.: On Gorenstein projective, injective and flat dimensions---a functorial description with applications. J. Algebra 302 (2006), 231-279. | DOI | MR | Zbl

[2] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra, de Gruyter Exp. Math. Walter de Gruyter and Co., Berlin. (2000). | MR

[3] Enochs, E. E., Iacos, A., Jenda, O. M. G.: Closure under transfinite extensions. Illinois J. Math. 51 (2007), 561-569. | DOI | MR

[4] Holm, H.: Gorenstein homological dimensions. J. Pure Appl. Algebra 189 (2004), 167-193. | DOI | MR | Zbl

[5] Holm, H., Jørgensen, P.: Cohen-Macaulay homological dimensions. Rend. Semin. Mat. Univ. Padova 117 (2007), 87-112. | MR

[6] Holm, H., Jørgensen, P.: Semi-dualizing modules and related Gorenstein homological dimensions. J. Pure Appl. Algebra 205 (2006), 423-445. | DOI | MR

[7] Holm, H., White, D.: Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47 (2007), 781-808. | DOI | MR | Zbl

[8] Kasch, F.: Modules and Rings. London Math. Soc. Monogr. Academic press, London (1981). | MR | Zbl

[9] Lam, T. Y.: Lecture on Modules and Rings. Springer Verlag, New York (1999). | MR

[10] Yang, X., Liu, Z.: Gorenstein projective, injective and flat modules. J. Aust. Math. Soc 87 (2009), 395-407. | DOI | MR

[11] Osborne, M. S.: Basic Homological Algebra. Graduate Texts in Mathematics, Springer, New York, Berlin (2000). | MR | Zbl

[12] Park, S., Pusan, E. C.: Injective and projective properties of $R[x]$-modules. Czech. Math. J. 54 (2004), 573-578. | DOI | MR

[13] Rotman, J. J.: An Introductions to Homological Algebra. Academic Press, New York (1979). | MR

[14] Sazeedeh, R.: Strongly torsion free, copure flat and Matlis reflexive modules. J. Pure Appl. Algebra 192 (2004), 265-274. | DOI | MR | Zbl

[15] Trlifaj, J.: Ext and inverse limits. Illinois J. Math. 47 (2003), 529-538. | DOI | MR | Zbl